Abstract

This paper presents an approximate analytical model of the dynamics of a tapered fly line during a standard overhead cast. During casting, the line forms a nonlinear propagating wave that is frequently referred to as a ‘loop’ by fly casters. The geometry of the loop is described by three distinct parts: a straight bottom segment (attached to a stationary fly rod), a semi-circular segment that is propagating (i.e. the loop), and a straight top segment that is also propagating, (i.e. the traveling line). A fly (particle) is attached at the end of the traveling line. A work-energy balance yields the velocity of the fly as a function of the length of the traveling line. For a uniform fly line (level line), a closed-form solution is found, while for a tapered fly line, the solution is obtained by quadrature. A critical loop diameter arises in the analysis, and it determines whether the final velocity of the fly is greater or lesser than the initial velocity of the traveling line. The analytical solutions are critically compared against numerical solutions of a general model for fly line dynamics that relaxes many of the assumptions employed in the analytical model. The agreement between the two solutions remains close during the loop propagation phase, provided a significant amount of fly line remains in the traveling line. However, as the traveling line vanishes and the loop ‘turns over’, the two solutions diverge abruptly due to the many simplifying assumptions employed in the analytical model. Verf.-Referat